John has been accused of murder and the police have found DNA evidence at the scene. The probability of a DNA match given that a person is innocent is 1/100,000. The probability of a DNA match given that a person is guilty is 1. John lives in a city where there are 100,000 people who could have committed the crime. Unfortunately, the outcome of the DNA match to John has been positive. What is the probability of John being guilty given the outcome of the DNA test? I don't understand that if the probability that a DNA matched given a person guity is 1, how come he/she can be innocent, why the 1/100000 can still happen. And does anybody think 'the 100000 people in John's city' this condition is useless? anyway, I think the answer is 99999/100000, cause ignore whether John is guilty, he still have 1/100000 probability can be innocent, is it right?